3 problems

Let $f:X\to B$ be a stable family of polarized Calabi–Yau varieties, where $B$ is a smooth disc. Assume that the central fiber is a stable variety as a polarized Calabi–Yau variety…

Let $f:X\to B$ be a stable family, and let the Weil–Petersson metric, or its logarithmic version, be the metric associated with the family. Assume that the central fiber is also a…

Let $f:X\to B$ be a family admitting a relative Kähler–Einstein metric. A family is called stable in the sense of Alexeev and Kollár–Shepherd-Barron when it satisfies the correspon…